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CENTER OF MASS AND MOMENT OF INERTIA     15!
The distance of the element of mass from the axis is y, therefore substi tuting in equation (II) these expressions for dm and its distance from th axis we obtain
J =   f 7/2 . era dy
JQ
for the desired moment of inertia. The limits of integration are differeo from those in equation (II) because the independent variable is change from m to y.
2. Find the moment of inertia about the cc-axis of a lamina which i bounded by the parabola x* = 2 py and the straight line y = a.
fa) Choosing a horizontal strip for the element of mass we have
dm = (7  2 x dy,
But
(b) We can also take an element of the strip for the element of mas in which case we have
dm  or dx dy.
= f cr a3 V2 pa, = f ma2.